Serre's problem on projective modules
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The work Serre's problem on projective modules represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.
The Resource
Serre's problem on projective modules
Resource Information
The work Serre's problem on projective modules represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Serre's problem on projective modules
 Statement of responsibility
 TsitYuen Lam
 Subject

 Commutative algebra
 Commutative algebra
 Commutative algebra
 Geometry, Algebraic
 Geometry, Algebraic
 Geometry, Algebraic
 Géométrie algébrique
 Modules projectifs (Algèbre)
 Projective modules (Algebra)
 Projective modules (Algebra)
 Projective modules (Algebra)
 SerreVermutung
 Algèbre commutative
 Anéis e álgebras comutativos
 Language
 eng
 Summary
 "Serre's Conjecture", for the most part of the second half of the 20th century,  ferred to the famous statement made by J. P. Serre in 1955, to the effect that one did not know if ?nitely generated projective modules were free over a polynomial ring k[x ,. . . ,x], where k is a ?eld. This statement was motivated by the fact that 1 n the af?ne scheme de?ned by k[x ,. . . ,x] is the algebrogeometric analogue of 1 n the af?ne nspace over k. In topology, the nspace is contractible, so there are only trivial bundles over it. Would the analogue of the latter also hold for the nspace in algebraic geometry? Since algebraic vector bundles over Speck[x ,. . . ,x] corre 1 n spond to ?nitely generated projective modules over k[x ,. . . ,x], the question was 1 n tantamount to whether such projective modules were free, for any base ?eld k. ItwasquiteclearthatSerreintendedhisstatementasanopenproblemintheshe theoretic framework of algebraic geometry, which was just beginning to emerge in the mid1950s. Nowhere in his published writings had Serre speculated, one way or another, upon the possible outcome of his problem. However, almost from the start, a surmised positive answer to Serre's problem became known to the world as "Serre's Conjecture". Somewhat later, interest in this "Conjecture" was further heightened by the advent of two new (and closely related) subjects in mathematics: homological algebra, and algebraic Ktheory
 Cataloging source
 GW5XE
 Dewey number
 516.3/5
 Index
 index present
 LC call number
 QA247.3
 LC item number
 .L35 2006
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Springer Monographs in Mathematics,
Context
Context of Serre's problem on projective modulesWork of
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